An explosion in the number of wireless broadband users has led to a severe spectrum shortage in the conventional cellular bands. The demand for cellular data services is expected to grow at a staggering rate, necessitating orders of magnitude increases in wireless capacity. Millimeter wave (mmW) frequencies at 28, 38, and 60 GHz have been attracting growing attention as a possible candidate for next-generation microcellular networks. This band offers orders of magnitude greater spectrum and also allows for building high dimensional antenna arrays for further gains via beamforming and spatial multiplexing. Devices based on mmW have already hit the market, but are limited by their use of highly directional horn antennas to enable short-range, line-of-sight links, within a controlled and static environment, such as in a data center. Since such an environment and conditions are very difficult—if not impossible—to achieve in a practical system implement, there is a need for building mmW systems “in the wild,” e.g., where line-of-sight is not always available, SNRs are lower, mobility is enabled, and the use of static directional antennas is infeasible. Exemplary embodiments of such mmW systems can be based on orthogonal frequency division multiplexing (OFDM) technology that is known to persons skilled in the art. Other exemplary embodiments can be based on Orthogonal Time Frequency & Space (OTFS)—a technique developed by Cohere Technologies and known to skilled persons—that transforms information carried in a delay-Doppler domain pair (also referred to as a “coordinate system”) to the time-frequency domain pair utilized by modulation schemes such as OFDM.
One of the biggest challenges in building such real-world, systems is that frequency offsets in the received signal are unavoidable. Such frequency offsets can be caused by phase noise, imperfect oscillators, Doppler shifts, or a combination of these factors. These offsets have a deleterious effect on the wireless link quality, especially for OFDM and OTFS systems. Frequency offsets that are large (but stable) can easily be corrected by existing baseband processing techniques. However, rapidly varying offsets cannot be corrected efficiently, leading to non-trivial residual offsets. These residual offsets lead to inter-carrier-interference (ICI), which causes the OFDM subcarriers to lose their orthogonality. This problem is exacerbated when the symbol durations are longer, because the oscillators exhibit larger drifts over larger time-scales. The end result is increased symbol error rates.
Moreover, the effects of frequency offsets can be exacerbated for systems with higher operating frequencies, such as mmW systems. Exemplary effects of frequency offset on a received symbol constellation are illustrated in FIG. 3 for two cases: (a) negligible frequency offsets on a 2.4-GHz wireless link, and (b) significant frequency offsets on a mmW (e.g., 60-GHz) wireless link. While the receiver can easily detect the received symbols in FIG. 3(a), the frequency offset in FIG. 3(b) can lead to high symbol error rate. Furthermore, frequency offsets in mmW systems can exhibit not only high magnitudes (e.g., FIG. 3(b)) but also high variations over time-scales as short as a few microseconds. Accordingly, there exists a need to mitigate these large, highly-variable offsets such that the residual is small enough to maintain both the orthogonality of the OFDM subcarriers and the resulting error rate within acceptable bounds.
There are several existing techniques that fall short of meeting this need. Equalization is an exemplary frequency-domain technique that relies on known pilot symbols to be scattered throughout the data symbols in the received data packet. By estimating the channel (e.g., the effects of the transmission medium and the receiver) at these pilot locations, the receiver can determine the channel at non-pilot locations (through interpolation) and decode the data symbols by removing the channel estimates from the received signal. However, equalization is unable to cope with the magnitude of phase noise in mmW systems.
Reference phase tracking is another exemplary frequency-domain technique in which a known QPSK pilot signal (“reference”) is applied to a particular subcarrier in every transmitted OFDM symbol. It estimates the phase rotation that the reference in symbol i has undergone relative to the reference phase observed in the previous symbol i−1. Once this phase rotation is measured for the reference, all the data-bearing subcarriers in symbol i are de-rotated by the same amount. Although this technique works well with small amounts of phase noise, the OFDM subcarriers lose their orthogonality as the phase noise is increased, and irreversibly interfere with each other before this technique can be applied.
Schmidl-Cox is an exemplary time-domain technique that measures the frequency offset on a per-packet basis using two reference OFDM symbols, and applies the correction to the remainder of the packet in the time domain, thereby eliminating ICI. This technique works well for large frequency offsets, but requires that they be relatively stable. As noted above, frequency offsets in mmW systems change significantly even on a per-symbol basis, rendering this technique incapable of correcting ICI.
Another exemplary method utilizes a feedback tracking loop comprising two components: a) frequency offset measurement, and b) frequency offset correction. Offsets can be measured either in the time domain (using the cyclic prefix), or in the frequency domain (using reference pilot symbols). In a closed loop system, this offset can be fed back to a numerically controlled oscillator (NCO), which can apply the correction in the time domain. If the offsets are stable, this technique can provide good gains, very similar to Schmidl-Cox. Since the feedback loop can be engineered to be quicker than the packet duration (unlike Schmidl-Cox), this technique can provide some gains over Schmidl-Cox.
The general structure of an exemplary feedback tracking loop is shown in FIG. 1. Signal 101 is a complex baseband (or intermediate frequency) time-domain sampled signal. These samples can be multiplied with signal 109 using complex multiplier (or digital mixer) block 102, resulting in signal 103. The initial value in signal 109 can be 1+0i. The frequency offset in signal 103 can be measured by block 104 using any measurement technique including, but not limited to: a) measurement in the time-domain using the cyclic prefix, or b) converting signal 103 to a frequency domain and measure the frequency offset using pilot symbols or reference subcarriers. The offset value calculated by block 104 can be communicated using signal 105 to block 106, which can be a moving (or weighted) average filter. The filter output 107 can be the average measured frequency offset, and can be fed into block 108, an exemplary numerically controlled oscillator. Block 108 produces a sampled complex sinusoid (signal 109), the frequency of which can be substantially the negative of the frequency of signal 107. Frequency correction signal 109 can be digitally mixed with subsequent values of signal 101. Similar prior art systems applied the frequency correction in analog, in which NCO 108 and digital mixer 102 can be replaced by a voltage controlled oscillator (VCO) and analog mixer, respectively
For correction in either digital or analog, this feedback tracking loop technique illustrated by FIG. 1 works well even for large offsets so long as they are stable. However, the problem with highly varying offsets is that by the time the offsets are calculated on signal 103 and the correction signal 109 is produced, the offsets would have changed significantly. Hence, there is need for a better technique to estimate and/or correct these frequency offsets when they vary more rapidly.
Since the frequency offset varies widely over a symbol period in an OFDM mmW system, symbols of shorter durations (i.e., smaller sizes of the FFT and inverse FFT used for demodulation and modulation, respectively) can be more resilient to phase noise. However, merely using a smaller symbol or FFT size is not practical. Outdoor mmW wireless links can have delay spreads as large as 300 ns. The cyclic prefix therefore should be at least this length in order to mitigate inter-symbol-interference (ISI). Reducing the overall symbol length (including the cyclic prefix) causes the cyclic prefix—which comprises overhead not usable for data symbols—to consume a larger portion of the symbol. For example, a cyclic prefix of 40 samples long (about 300 ns at 130×106 samples/s), FFT sizes of 128, 256, 512, and 1024 have their cyclic prefix overheads as approximately 31.25%, 15.6%, 7.8%, and 3.9% respectively. As such, merely reducing the FFT size is not a practical solution for mitigating frequency offset in mmW OFDM systems.
Thus, there may be a need to address at least some of the inadequacies, issues, and/or concerns with existing mmW frequency offset correction techniques described above.